I occasionally feature domain names on Twitter. If you do so I think it is important to make them attractively presented. Also, although some on Twitter use it only for promoting domain names, I think this gets tired fast and people will stop following you. I think if you have a mix of interesting and valuable content, with the occasional featured domain, most people will accept, or even appreciate, that.
I have not yet used LinkedIn for domains but see that potentially it could be very valuable, and know some on here that use it effectively.
For a non-domain purposes I have bought Facebook ads a few times with mixed success. It is effective if you want to market to a specific demographic, and as such it might be good for geo or specialized type domains.